Finite Impulse Response Systems Research Articles

Detection of data tampering attack in FIR system identification with binary-valued observations

This paper addresses the security detection of data tampering attack in identification of finite impulse response systems with quantized observations. First, we designed a detection algorithm for data tampering attack based on the prior information of the system and gave its online detection form. Second, the introduction of the concepts of the false judgment rate and the missed judgment rate gave a specific evaluation index for the performance of the detection algorithm. Considering the high nonlinearity of binary quantized and the difficulty of obtaining distribution function, we provided calculation methods for two indexes and gave expressions under large samples. Then, the effects of the data length, the prior information of the system parameter, and the attack strategy on the detection algorithm are discussed in this paper. Finally, the theoretical results are verified by numerical simulation.

Binary observation‐based identification for finite impulse response systems under denial of service attacks

SummaryThis article considers the parameter identification problem for the finite impulse response system based on binary observations under denial of service attacks. First, in addition to designing the identification algorithm for the unknown parameter, and its convergence is verified, simultaneously obtaining the asymptotic normality. Then, based on the convergence speed of the identification algorithm and the covariance matrix of the estimation error, the optimal attack strategy problem is transformed into an optimization problem with constraints, then the optimal solution is given. Furthermore, a defense strategy with dual time‐scale input design method is proposed and its effectiveness is demonstrated. Finally, numerical simulations are applied to evidence the correctness of the raised method.

FIR system identification under congruential summation-triggered communication scheme with binary observations

With the development of information technology, the amount of data transmitted in the network is getting larger and larger, and how to effectively utilize the communication resources has become the focus of a lot of research. In the framework of Finite Impulse Response (FIR) systems, this paper proposes a congruential summation-triggered communication scheme based on the cumulative effect of binary-valued observations to address the parameter identification problem, and its communication rate is derived. Then, the parameter estimation algorithm is designed under periodic input, and its strong convergence is proved, while an index is established to characterize the convergence performance of the algorithm. Furthermore, the trade-off problem between algorithm performance and communication resource is modeled as an optimization problem with constraints, and its explicit solution is given. Finally, numerical simulations are performed to verify the correctness and reasonableness of the algorithm.

Binary observation‐based FIR system identification under sequence denial of service attacks

AbstractDue to the close interaction between computing, sensing, communication, and driving of the cyber‐physical system (CPS), which makes it highly vulnerable to cyber attacks, the security of CPS has attracted wide attention. In the article, we discuss the system identification problem of the finite impulse response system under sequence denial of service attacks. The identification algorithm of the unknown parameter is designed under binary observations, and its convergence performance is analyzed. The optimal attack strategy problem is modeled as a optimized problem with constraints based on the covariance matrix of estimation error, the solution method and implementation algorithm are given. From the perspective of the defender, an encryption‐type defense algorithm is designed, and then the optimal defense strategy is presented. The numerical simulation is used to verify the validity of the proposed method.

Identification of FIR Systems With Binary-Valued Observations Against Data Tampering Attacks

This article addresses the security issue against data tampering attacks in the identification of finite impulse response (FIR) systems with binary-valued observations. First, the data tampering rate and estimation error caused by the network attack are derived. From the perspective of the attacker, it is investigated how to achieve the maximum attack effect with the minimum energy. Second, the compensation-type defense scheme is designed. Under this, the identification algorithm is constructed, and its strong convergence is proved. Taking the covariance matrix of the estimation error as the performance index, the optimal defense scheme is given. Finally, the results obtained are verified by simulation example.

Recursive system identification method from binary input/output measurements

AbstractThis paper presents two online identification algorithms of finite impulse response (FIR) systems using binary measurements both on the input and on the output. These algorithms are based on the least mean square (LMS) technique and on the estimation of the correlation functions of the input and output from binary data. Note that the second algorithm is a simplified version of the first one in the case of a white noise on the input. The convergence and variance analyses are provided. A numerical example is given to demonstrate the effectiveness of the proposed algorithms.

Identification of FIR systems with binary-valued observations against denial-of-service attacks

DoS (Denial-of-Service) attack is a very common network attack, under which it is of great practical significance to study the system performance. This paper addresses the security problem in the identification of FIR (Finite Impulse Response) systems with binary-valued observations when the data is under DoS attacks in the process of transmission. From the attacker’s point of view, the optimal attack strategy to maximize the estimation error is given, where the attack is constrained by the average and the maximum energies. From the defender’s point of view, the encryption-type defense scheme is proposed, and the sufficient and necessary conditions are given to make the algorithm consistent. The effectiveness of the conclusion is verified by numerical simulation. Finally, the correctness of the obtained conclusion is verified by numerical simulation.

Either-or communication-based identification of FIR systems with binary-valued observations and channel uncertainty

Event-triggered mechanism can effectively save communication resources, however, when it encounters channel uncertainty, the remote receiver cannot distinguish between “the sender did not send data” and “the sender sent data but the data lost” when it does not receive data, which causes that it is difficult to make full use of the information provided by the event-triggered mechanism. This paper addresses the identification of FIR (Finite Impulse Response) systems with binary-valued observations and either-or communication mechanism when the packet loss probability is known and unknown respectively. When the packet loss probability is known, it is used for compensation in the parameter estimation. An online identification algorithm is proposed, its strong convergence is proved, and its asymptotic normality is given. Furthermore, how does the packet loss probability affect the algorithm performance is discussed. When the packet loss probability is unknown, an identification algorithm is proposed to jointly estimate it and unknown system parameters by redesigning the either-or communication mechanism. The strong convergence of the algorithm is shown. The tradeoff between the communication rate and the convergence performance of the identification algorithm is modelled as a constrained optimization problem, and its solution is obtained. The rationality of theoretical results is verified by numerical simulation.

DoS attack detection in identification of FIR systems with binary‐valued observations

AbstractTimely and effective detection of malicious attacks is a primary problem in cyber‐physical system security. This paper studies the detection of DoS (denial of service) attacks in identification of FIR (finite impulse response) systems with binary‐valued observations. Based on the prior information of the system, an attack detection algorithm is designed, and its online form is given. The detectability is discussed for the ability of detection algorithm, and the necessary and sufficient condition for the attack strategy to be detectable is obtained. The concepts of the missed detection rate and false alarm rate are introduced, and their calculation methods and approximate formulas under large samples are provided. Furthermore, it is analyzed the influence of prior information of system parameters and data length on the performance of detection algorithm. The rationality of theoretical results is verified by numerical simulation.

Model recovery for multi-input signal-output nonlinear systems based on the compressed sensing recovery theory

This paper considers the parameter and order estimation for multiple-input single-output nonlinear systems. Since the orders of the system are unknown, a high-dimensional identification model and a sparse parameter vector are established to include all the valid inputs and basic parameters. Applying the data filtering technique, the input-output data are filtered and the original identification model with autoregressive noise is changed into the identification model with white noise. Based on the compressed sensing recovery theory, a data filtering-based orthogonal matching pursuit algorithm is presented for estimating the system parameters and the orders. The presented method can obtain highly accurate estimates from a small number of measurements by finding the highest absolute inner product. The simulation results confirm that the proposed algorithm is effective for recovering the model of the multiple-input single-output Hammerstein finite impulse response systems.

Gaussian Process based Feedforward Control for Nonlinear Systems with Flexible Tasks: With Application to a Printer with Friction

Feedforward control is essential to achieving good tracking performance in positioning systems. The aim of this paper is to develop an identification strategy for inverse models of systems with nonlinear dynamics of unknown structure using input-output data, which can be used to generate feedforward signals for a-priori unknown tasks. To this end, inverse systems are regarded as noncausal nonlinear finite impulse response (NFIR) systems, and modeled as a Gaussian Process with a stationary kernel function that imposes properties such as smoothness. The approach is validated experimentally on a consumer printer with friction and shown to lead to improved tracking performance with respect to linear feedforward.

Learning low-dimensional separable decompositions of MIMO non-linear systems

We present a new internal structure exploration method developed for the multiple-input multiple-output (MIMO) dynamical systems with finite memory and almost arbitrary non-linear characteristic. The proposed Double Separation Algorithm applies distance correlation screening for pre-selection of those system inputs that contribute to the consecutive outputs and, based on the first-stage inference outcomes, estimates projection coefficients sensitive to the existence of additive system sub-characteristics. In effect, the proposed approach allows for effective exploration of the internal system structure. A numerical experiment on an MIMO nonlinear finite impulse response (NFIR) system illustrates the ability of the proposed approach to indicate which of the system inputs contribute to which of the system outputs. The experiment also illustrates the ability of the approach to detect which of the nonlinear sub-characteristics, recovered in the first stage of the approach, can be separated into a sum of lower-dimensional sub-characteristics.

A unified identification algorithm of FIR systems based on binary observations with time-varying thresholds

This paper is concerned with parameter estimation of finite impulse response (FIR) systems with binary observations. Combining a suitable design of the time-varying thresholds, a kind of sign-error type unified algorithm with projection is investigated for either deterministic systems or stochastic systems. The convergence properties of the studied algorithm are established under bounded persistent excitations. Specifically, for the case without noise, the square convergence rate is proved to be close to O1k2 with respect to the time step k. For the case with bounded noises, the upper bound of the estimation error is obtained, which depends on the bound of the noises and the lower bound of the input persistent excitation condition. For the case with independent and identically distributed (i.i.d.) stochastic noises, the estimate is shown to converge to the true parameter in the sense of mean square and almost surely. Besides, the mean square convergence rate of the estimation error is of the order O1k. Numerical examples are supplied to demonstrate the theoretical results.

Application of regularized Savitzky–Golay filters to identification of time-varying systems

Savitzky–Golay (SG) filtering is a classical signal smoothing technique based on the local least squares approximation of the analyzed signal by a linear combination of known functions of time (originally — powers of time, which corresponds to polynomial approximation). It is shown that the regularized version of the SG algorithm can be successfully applied to identification of time-varying finite impulse response (FIR) systems. Such a solution is possible owing to the recently proposed preestimation technique, which converts the problem of identification of a time-varying FIR system into the problem of smoothing of the appropriately generated preestimates of system parameters. The resulting fast regularized local basis function estimators, optimized using the empirical Bayes approach, have very good parameter tracking capabilities, favorably comparing with the state-of-the-art in terms of accuracy, computational complexity and numerical robustness.

Blind Signal Estimation Using Structured Subspace Technique

This brief addresses the blind signal estimation of a single input multiple output (SIMO) finite impulse response (FIR) system. The proposed method estimates directly the input signal with no need for the channel estimation stage or estimation of the second-order statistics. This is achieved by exploiting the Toeplitz structure inherent in the signal’s linear model, to build a quadratic cost function. Such methods are needed to lessen the latency and wave the error propagation phenomena. The simulation results are compared to other methods and are shown to highlight appealing advantages under adverse scenarios, specifically, short-burst communications and poor channel diversity.

Variational Bayesian inference for the identification of FIR systems via quantized output data

For identifying the parameters in finite impulse response (FIR) systems via the quantized output, existing expectation maximization (EM) methods are involved with the intractable integrals. To overcome the above shortcoming, this paper proposes an approach referred to as explicit EM (EEM). First, we fit the quantized output data by a linear Gaussian regression distribution with some compensation parameters. As a result of the linear Gaussianity, the posterior of the excited output can be explicitly computed, so that EEM has the less computation burden than the existing EMs. Second, through optimizing these compensation parameters by resorting to variational Bayesian inference, the intrinsic distribution of the quantized output can be well fitted with guaranteed identification accuracy. Third, the linear Gaussian regression distribution is independent of the specific quantization function form, which enables EEM applicable for different quantization forms. Finally, the simulation demonstrates the feasibility and effectiveness of the proposed approach.

Asymptotically Efficient Recursive Identification of FIR Systems With Binary-Valued Observations

This paper considers the identification problem of finite impulse response (FIR) systems with binary-valued observations under the assumption of fixed threshold and bounded persistently excitations. A recursive projection algorithm is constructed to estimate the unknown parameter. For first-order FIR systems, the convergence properties of the algorithm are analyzed theoretically. With mild conditions on the weight coefficients in the parameter update, the algorithm is proved to be convergent in mean square and the convergence rate can be the reciprocal of the number of observations, which has the same order as the optimal estimation when the system output is exactly known. Furthermore, it is also shown that the Cramer–Rao (CR) lower bound is achieved asymptotically with proper weight coefficients, which indicates that the algorithm is optimal in the sense of asymptotic efficiency. Some numerical examples are simulated to demonstrate the effectiveness of the proposed algorithm in both first-order and high-order FIR systems.

Finite impulse response models: A non-asymptotic analysis of the least squares estimator

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction bounds for the least squares estimator of the parameters. Our results are based on two concentration inequalities on the norm of sums of dependent covariate vectors and on the singular values of their covariance operator that are of independent value on their own and where the dependence arises from the time shift structure of the time series. These results generalize the known bounds for the independent case.

Iterative parameter and order identification for fractional‐order nonlinear finite impulse response systems using the key term separation

SummaryThis article considers the parameter estimation for a fractional‐order nonlinear finite impulse response system with colored noise. For the fractional‐order systems, the challenge and difficulty are to identify the order and parameters of the systems simultaneously under colored noise disturbances. In order to reduce the problem of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the separation of the key term separation. A key term separation auxiliary model gradient‐based iterative algorithm is derived by using the negative gradient search. Meanwhile, to achieve the higher estimation accuracy, we propose a key term separation auxiliary model multiinnovation gradient‐based iterative algorithm by utilizing the multiinnovation theory. Finally, the simulation results test the effectiveness of the proposed algorithms.

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

SummaryIn this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener‐FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener‐FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.